One of the more difficult concepts for middle school students to master is integers. Specifically, adding and subtracting integers. Even when the concept is introduced with concrete and tangible examples, the students still struggle with the often counterintuitive nature of negative numbers.
You see, in elementary school, they are taught that addition always results in more and subtraction, less. But once those numbers become negative, the results are often reversed.
One of the ways I help them remember the rules for adding and subtracting integers in by relating it to relationships:
When a good person comes into your life, it improves the value.
When a good person leaves your life, it reduces the value.
When a bad person comes into your life, it reduces the value.
And the one they have the hardest time understanding…
When a bad person leaves your life, it increases the value.